f(x)=8x^2-5x eching

$$f ( x ) = 8 x ^ { 2 } - 5 x$$

Omil

$$x\left(8x-5\right)$$

Yechim qadamlari

x omili.

$$x\left(8x-5\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$8x^{2}-5x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2\times 8}$$

\left(-5\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±5}{2\times 8}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±5}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{5±5}{16}$$

x=\frac{5±5}{16} tenglamasini yeching, bunda ± musbat. 5 ni 5 ga qo'shish.

$$x=\frac{10}{16}$$

\frac{10}{16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{8}$$

x=\frac{5±5}{16} tenglamasini yeching, bunda ± manfiy. 5 dan 5 ni ayirish.

$$x=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$x=0$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5}{8} ga va x_{2} uchun 0 ga bo‘ling.

$$8x^{2}-5x=8\left(x-\frac{5}{8}\right)x$$

Umumiy maxrajni topib va suratlarni ayirib \frac{5}{8} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$8x^{2}-5x=8\times \frac{8x-5}{8}x$$

8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$8x^{2}-5x=\left(8x-5\right)x$$

Baholash

$$x\left(8x-5\right)$$